Question

If a metal crystallises in bcc structure with edge length of unit cell 4.29 × 10^-8 cm the radius of metal atom is ______.

Options

• 3.2 × 10^-7 cm

• 1.86 × 10^-8 cm

• 1.07 × 10^-7 cm

• 1.07 × 10^-8 cm

Answer 1

If a metal crystallises in bcc structure with edge length of unit cell 4.29 × 10^-8 cm the radius of metal atom is 1.86 × 10^-8 cm.

Explanation:

The relation between edge length and radius of an atom in a bcc structure is related as:

r = ${\displaystyle \sqrt{3}/4\text{a}}$

Given, a = 4.29 × 10^-8 cm

For bcc structure,

r = ${\displaystyle \frac{\sqrt{3}}{4}\text{a}=\frac{\sqrt{3}}{4}\times 4.29\times {10}^{-8}\text{cm}}$

${\displaystyle =1.857\times {10}^{-8}\text{cm}}$

= 1.86 × 10^-8 cm